It's difficult to write about the Internet, because its shape is changing so rapidly. Bruce Sterling's 1993 article, "A Short History of the Internet," is already out of date. It makes no mention of the World-Wide Web (WWW), for instance. It is, however, an excellent account of how the Internet came to be.
Hobbes' Internet Timeline presents the history of the Internet in summary form almost to the present day. Look especially at the events of the last few years, and the charts at the end of the timeline, which show the recent exponential growth of the Internet.